I have some points in 3d and want to do a sort of extrapolation on them. My points are in a regular x and y grid and have some splits. I want to extraploate points beyond the splits. I copied a simplified data set having three splits. I extrapolate the end side of the first split, both sides of the middle split and front side of the third one. In case of 10 splits I extrapolate end side of the first, both sides of split numbers 2 to 9 and front side of the last. These are my coordinates (x, y and z):
surf_points=[[np.array([[1.,19.,4.],[1.,20.,4.],[2.,19.,4.5],[2.,20.,4.5],[3.,20.,4.]]),\
np.array([[4.,19.,3.2],[4.,20.,3.],[5.,19.,3.],[5.,20.,3.1],[6.,19.,3.1],[6.,20.,3.1]]),\
np.array([[7.,19.,4.1],[7.,20.,4.2]])]]
At the moment, each split is sorted firstly in x direction, then in y direction. I change it to be sorted firstly based on y and then x using this solution. Then surf_points will be:
[[np.array([[1.,19.,4.],[2.,19.,4.5],[1.,20.,4.],[2.,20.,4.5],[3.,20.,4.]]),\
np.array([[4.,19.,3.2],[5.,19.,3.],[6.,19.,3.1],[4.,20.,3.],[5.,20.,3.1],[6.,20.,3.1]]),\
np.array([[7.,19.,4.1],[7.,20.,4.2]])]]
First splits extrapolation
For first split I want to add two points at the end of each y grid. First y grid is 19 and second one is 20. x and y of new points are fixed and defined: (3.,19.) and (4.,19.). z value is calculated from the previous two points existing in each y grid. In case of having only one point in the grid, I simply copy z of that single point. First y grid has two points with z values 4. and 4.5. The first extrapolated point is the third one in this grid and its z will be calculate as 4.5 + (4.5-4)/2 = 4.75 (z of last point + (z of last point - z of one point before the last)/2) and for the second extrapolated point I update the the last and one before last points to have it as 4.75 + (4.75-4.5)/2 = 4.875. So, two extrapolated point of the first y grid will be (3.,19.,4.75) and (4.,19.,4.875). I do the same for second y grid (20). This grid has three points and two added points will be (4.,20,3.75 #4+(4-4.5)/2) and (5.,20, 3.625# 3.75+(3.75-4.)/2). These four points will be added at the end of first split.
Middle splits extrapolation
For middle splits I add four points to front side and four point to end side. The end side is exactly like end side of first split. For front side x and y values of extrapolated point will be less than existing one. They will be (2.,19.) and (3.,19.) in first y grid and (2.,20.) and (3.,20.) in second y grid. I start to calculate the z firstly for second point as (z of first point + (z of first point - z of second point)/2). It will be calculated from existing next two points as 3.2 + (3.2-3.)/2. which makes 3.3 and then use this 3.3 value for calculating z value of the first point in this grid 3.3 + (3.3-3.2)/2. which makes 3.35. I do the same for the second y grid.
Last splits extrapolation
For the last split I want to copy what I did for the front side of the second split, but it has only one point in each y grid and I only copy that value for extrapolated ones.
Finally new extrapolated points should be added to previous ones and I want my list to be as:
all_points=[[np.array([[1.,19.,4.], [1.,20.,4.], [2.,19.,4.5], [2.,20.,4.5], [3.,20.,4.],\
[3.,19.,4.75], [4.,19.,4.875], [4.,20,3.75], [5.,20, 3.625]]),\
np.array([[2.,19.,3.3], [3.,19.,3.35], [2.,20., 2.923], [3.,20., 2.95],\
[4.,19.,3.2], [4.,20.,3.], [5.,19.,3.], [5.,20.,3.1], [6.,19.,3.1], [6.,20.,3.1],\
[7.,19.,3.15], [8.,19.,3.175], [7.,20., 3.1], [8.,20., 3.1]]),\
np.array([[5.,19.,4.1], [6.,19.,4.1], [5.,20.,4.2], [6.,20.,4.2],\
[7.,19.,4.1], [7.,20.,4.2]])]]
To clarify my problem, a fig is uploaded. In the fig extrapolated points of each split are shown with differen colurs and symbols. I do appreciate any help to write my idea as an algorithm in python.
